[seqfan] Re: Correcting A002932 (n-step walks on square lattice)

Christopher Gribble chris.eveswell at virgin.net
Mon Nov 22 16:16:29 CET 2010


I have been working with Tom Young on a set of related problems for some
time.  I would be most grateful if you could send me a copy of the Fisher
and Hiley reference as I do not have access to it.  I think that the title
of A002932 may need to be made more explicit, since it does not state
whether the lattice is bounded or not, and, if so, what form the boundary
takes. Of course, no restriction on path construction is mentioned either.
I have calculated many cases for the general bounded lattice problem with
the restriction you describe.  Perhaps we can compare notes.

Best regards,
Chris Gribble

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Joseph S. Myers
Sent: 22 November 2010 1:25 PM
To: seqfan at seqfan.eu
Subject: [seqfan] Correcting A002932 (n-step walks on square lattice)

A002932 is "Number of n-step walks on square lattice." - where there is a
restriction (see the Fisher and Hiley reference) that no lattice point
appears more than once in the path, and no two points in the path that are
not consecutive in the path may be adjacent in the lattice.

There are two entries in the "formula" section both of which are wrong - one
reporting an observed link to A001333 and the other giving an explicit
formula; they go wrong from the term with value 940 onwards, where both give
the value 956 instead.  (They would probably be correct if the adjacency
restriction was local, only relating to points 3 apart in the path, though I
haven't checked this.)

The last term given of the sequence, 396204, disagrees with my calculations;
I get 396172 although my program agrees with the earlier terms.  Before I
make corrections (and extensions - I have eight more
terms) to this sequence, could someone confirm whether they get the figure I
do or the figure in the sequence (which is accurately transcribed from the
Fisher and Hiley reference)?

Joseph S. Myers
jsm at polyomino.org.uk


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